Download Practice Test Ch. 4 Obtuse Triangle Trigonometry

FOM 11
Practice Test
Ch.4 – Trigonometry Name: ___________
Block: _____
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Calculate sin 16° to four decimal places. Predict another term that equals sin 16°.
a. –0.2756; sin 164°
b. 0.2756; sin 164°
c. 0.2756; –sin 16°
d. none of the above
____
2. Which law could you use to determine the unknown angle in this triangle?
a.
b.
c.
d.
____
the sine law only
neither the sine law nor the cosine law
the cosine law only
the sine law and the cosine law
3. Determine the unknown side length to the nearest centimetre.
a.
b.
c.
d.
4.4 cm
4.3 cm
4.6 cm
4.7 cm
____ . In ∆FGH, GH = 4.5 cm and G = 15°.
What is the height of the triangle from base GF?
a.
b.
c.
d.
1.5 cm
1.3 cm
1.2 cm
0.9 cm
Short Answer
. Write another term using the tangent ratio that is equivalent to tan 48°.
. Determine the unknown side length to the nearest tenth of a centimetre.
. Determine the unknown angle measure to the nearest degree.
. Determine the unknown angle measure to the nearest degree.
Problem
. In ∆QRS, q = 1.7 m, r = 4.3 m, and s = 5.6 m. Solve ∆QRS by determining the measure of each angle to the
nearest degree. Show your work and draw ∆QRS.
1. While golfing, Beth hits a tee shot from point T toward a hole at H. However, the ball veers 34° and lands at B.
The scorecard says that H is 250 m from T. Beth walks 120 m to her ball. Sketch a diagram of this situation.
How far, to the nearest metre, is her ball from the hole? Show your work.
1. A building is observed from two points (looking in the same direction), P and Q, that are 94.0 m apart. The
angle of elevation is 42° at P and 33° at Q. Sketch the situation. Determine the height of the building to the
nearest tenth of a metre.
1. An airplane is flying directly toward two forest fires. From the airplane, the angle of depression to one fire is
43° and 20° to the other fire. The airplane is flying at an altitude of 2500 ft. What is the distance between the
two fires to the nearest foot? Show your work.
FOM 11 Ch. 4 – Obtuse Triangle Trigonometry
Practice Test
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
B
C
A
A
A
C
PROBLEM
5.62 = 1.72 + 4.32 – 2(1.7)(4.3)Cos S
9.98 = -14.62 Cos S
-0.682… = Cos S
133.049 = S
133° = ∠S
12.
SHORT ANSWER
Find ∠R:
7. –tan 132°
8. Unknown Angle = 107°
.
.
.
∠R = 34°
∠Q = 180° – ∠R – ∠S
∠Q = 13°
x = 2.5 cm
9. Find Unknown Side:
a2 = (2.7)2 + (4.9)2 – 2(2.7)(4.9)Cos116
a = 6.549755762…
.
.…
Sin x = 0.3705…
x = 21.747
x = 22°
10. 2.62 = 4.42 + 5.72 – 2(5.7)(4.4)Cos x
-45.09 = -50.16Cos x
0.898… = Cos x
25.98 = x
26° = x
11. a is smaller than b
Find h:
h = bSinA = (7.5)Sin45
= 5.3 cm
h<a<b
∴ two triangles:
Find ∠B
.
∠B = 62° or 118°
13.
t2 = 1202 + 2502 – 2(120)(250) cos 34°
t = 164.796...
Beth's ball is 165 m from the hole.
(180 – 62)
16. Draw a rough (not-to-scale) sketch of the situation,
as shown. Determine the unknown angles using the
property that the measures of the angles in a triangle
sum to 180°. Let A and B represent the positions of
the fires.
14.
By the sine ratio
94.0
33 9
43 2500
+,
BD = 3665.397…
PR = 327.268…
By the sine law,
-+
3665.397 …
23
20
Sin 42 = .!…
AB = 4187.772
(327.268…)Sin 42 = 218.985
OR
The height of the building is 219.0 m.
tan 20 15.
2#
tan 43 AC = 345 AC = 6868.694
#
∠C = 29.249
= 29°
since Sin(x) = Sin(x – 180)
OR
∠C = 180 – 29
= 151°
∠B = 180 – 29 – 20
= 131°
OR
OR Sine Law
$
350
sin 131 sin 20
b = 772.32 m
BC = 345 BC = 2680.922
AB = AC – BC = 6868.694 – 2680.922
= 4187.772
The fires are 4188 ft apart.
∠B = 180 – 151 – 20
= 9°
Cosine Law
b2 = 5002 + 3502 – 2(500)(350)Cos 131
b = 775.96 m
2nd Triangle #
Cosine Law
b2 = 5002 + 3502 – 2(500)(350)Cos 9
b = 163.73 m
OR Sine Law
$
350
sin 9 sin 20
b = 160.08